Make frosting: In a large bowl using a hand mixer or the bowl of a stand mixer using the whisk attachment, beat butter and 2 1/2 cups powdered sugar. Add remaining lemon juice and zest and heavy cream and beat until combined, then beat in vanilla and salt. (Add remaining 1/2 cup powdered sugar as desired for texture and flavor.)

Place a dab of frosting on cake plate (to keep cake in place) and place parchment strips on each side of the cake plate. Place down first cake and top with frosting, then top with second cake and frost. Repeat with third cake and frost sides.

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